High Q optical microwave processor using hybrid delay-line filters

ABSTRACT

A hybrid active-passive signal bandpass filter comprising an active filter arranged in use to operate at a fundamental frequency which is a sub-multiple of a desired filter frequency of the bandpass filter, and a passive filter arranged in use to eliminate any pass bands in the frequency response of the active filter other than at the desired filter frequency for providing the pass band signal of the bandpass filter.

FIELD OF THE INVENTION

The present invention relates to the field of filtering and inparticular discloses an optical filtering method and apparatus.

BACKGROUND OF THE INVENTION

Photonic processors for microwave signal processing functions areattractive because of their very high time-bandwidth productcapabilities. Such processors can remove the bottlenecks caused bylimited sampling speeds in conventional electrical signal processors. Inaddition, they have excellent isolation, immunity to electromagneticinterference (EMI), and remove the limitations of Optical/Electrical andElectrical/Optical conversions for processing high speed signals thatare already in the optical domain. Photonic processors also have theability of attaining extremely high resolution and microwavefrequencies.

Recently, there has been considerable interest in photonic processingfor microwave filtering applications, and a variety of structures havebeen reported. A common objective is to increase the Q and frequencyselectivity of these filters. This is more difficult to realise forbandpass filters, because it requires an increase in the number of tapsin the discrete time signal processor. For this reason, passivestructures for photonic processors give limited Q values. Activestructures can achieve much higher Q values, but are limited by therequirement that they operate close to the lasing threshold. Also, thefundamental frequency and finesse of these filters is limited because ofthe minimum length of erbium fibre that can be used. Previously, thepresent inventors have reported an active photonic signal processor thatexhibits a Q of 325, however it is difficult to increase the Q furtherin this structure because of the onset of lasing.

SUMMARY OF THE PRESENT INVENTION

In accordance with a first aspect of the present invention, there isprovided an active-passive signal bandpass filter comprising:

an active filter an active filter arranged in use to operate at afundamental frequency which is a sub-multiple of a desired filterfrequency of the bandpass filter; and

a passive filter arranged in use to eliminate any pass bands in thefrequency response of the active filter other than at the desired filterfrequency for providing the pass band signal of the bandpass filter.

The active filter can comprise an infinite impulse response filter andthe passive filter can comprise a finite impulse response filter.

The active and passive filters can operate on photonic signals and aninput signal to the bandpass filter can comprise an optical inputsignal. The filter preferably operates at microwave frequencies and theinput signal can be created via the modulation of the optical signal bya microwave frequency optical oscillator.

The passive filter can comprise a plurality of passive filter elementseach comprising a notch filter which, in combination, have highattenuation characteristics for frequencies outside the desired filterfrequency and low attenuation of the desired filter frequency. Thenumber of passive filter elements can, for example, be 3.

The passive filter may be formed from optical fibre components.

Alternatively, the passive filter may be formed from optical planarintegrated circuits.

A post filter element can be further interconnected to the passivefilter, the post filter element providing for further rejection of nondesired filter frequencies.

The active filter may comprise an active delay line filter.

The active delay line filter can comprise an optical fibre whichcomprises two gratings that define a pass length between them, theoptical fibre being erbium doped and the active delay filter furthercomprising a pump laser for providing the gain of the active delay linefilter.

Alternatively, the active filter may comprise an optical planarintegrated circuit.

The optical planar integrated circuit may comprise optical waveguidesfor providing the delay function of the active delay line filter anddoped optical waveguides for providing the gain function of the activedelay line filter; and waveguide gratings in the optical waveguidesdefining a pass length therebetween.

The active filter may be a tunable active filter for wavelength tuningthe filter frequency of the filter.

In one embodiment, the tunable active filter may comprise chirpedgratings defining a plurality of path lengths, each path length beingassociated with a predetermined wavelength of a laser pumping the activedelay line filter.

This can enable the filter frequency to be changed.

The present invention may alternatively be defined as providing aphotonic processor having a quality factor in excess of about 325.

BRIEF DESCRIPTION OF THE DRAWINGS

Notwithstanding any other forms which may fall within the scope of thepresent invention, preferred forms of the invention will now bedescribed, by way of example only, with reference to the accompanyingdrawings in which:

FIG. 1 is a schematic illustration of a first embodiment;

FIG. 2a is a graph illustrating an active filter response;

FIG. 2b illustrates a computed filter response of a first embodiment;

FIG. 3 illustrates a graph of the filter response of the passivecomponents of the first embodiment;

FIG. 4 illustrates the calculated impulse response of the preferredembodiment;

FIG. 5 is a schematic illustration of a second embodiment;

FIG. 6 illustrates the measured frequency response of the active filterof the first embodiment;

FIG. 7 illustrates the measured frequency response of the firstembodiment, and

FIG. 8 illustrates the measured frequency response of the secondembodiment;

FIG. 9 illustrates a third embodiment.

DESCRIPTION OF THE PREFERRED AND OTHER EMBODIMENTS

1. Introduction

In the preferred embodiments, a new topology for a photonic signalprocessor is presented which overcomes previous limitations and enablesboth a high Q and a high frequency of operation to be obtained.

The structure of the preferred embodiment is based on a hybrid filterapproach which combines both active filter and passive filter sections.The active section is operated at a sub-multiple of the desired filterfrequency. Hence it can achieve a much narrower 3 dB bandwidth response,for a given gain margin. The passive sections are used to eliminate theintermediate peaks, and to select the multiple that corresponds to thedesired filter frequency. The advantages of this structure are that itenables a significant increase in Q to be obtained, it can function athigher frequencies, and it has a very robust operation. Using this newtopology, a very high resolution microwave signal filtering system wasconstructed with measured Q values of 801 for the hybrid processor. Anextension to this principle is also described as an alternativeembodiment and includes an additional passive optical stage, and resultsdemonstrate a narrowband filter response with a Q of 983.

The new hybrid active-passive photonic processor topology for microwavesignal filtering is presented in Section 2 below. The synthesisprocedure for designing the hybrid filter to obtain a specified filterfrequency is described in Section 3. Coherence effects are discussed inSection 4. The design of higher order passive filters to increase the Qof the hybrid filter are described in Section 5. Finally, Section 6describes experimental results on the hybrid processor, whichdemonstrate the high Q characteristics.

FIG. 1 illustrates a first embodiment 1 in which an RF input signal isinput 2 to an electro optic modulator 3 which modulates the intensity ofthe output from laser 4. The output from modulator 3 passes through afirst active filter section 5 before passing to a second passive filtersection 6. The active filter 5 comprises a series of Bragg gratings 8, 9on either side of an erbium doped fiber 10. The active filter acts as aninfinite impulse response filter. The output from active filter 5 isforwarded via circulator 10 to the passive filter 6 which consists of aseries of cascaded filters 11-13.

2. Hybrid Active-Passive Microwave Optical Filter Topology

Considering first the active filter 5 on its own, it includes a responsestructure as illustrated in FIG. 2a with its characteristics beingdefined by a first order peak 20 at frequency f_(1act) $\begin{matrix}{f_{1{act}} = \frac{c}{{nl}_{act}}} & \text{(EQ~~1)}\end{matrix}$

where l_(act) is the double pass length between the front 9 and rear 8gratings; and the 3 dB bandwidth of its response peaks 20 is given by$\begin{matrix}{{\Delta \quad f_{act}} = \frac{\arccos \quad \frac{{- 1} + {2G} - {0.25\quad G^{2}}}{G}}{\pi \quad T_{act}}} & \text{(EQ~~2)}\end{matrix}$

where T_(act)=n1 _(act)/c. Eq(2) is derived from a transfer functionanalysis of the active delay line, with first grating 9 reflectivity of50%, second grating reflectivity 8 of 100%, and a double pass gain of Gin the active fibre.

If we realise a fundamental frequency filter of f_(filter) directlyusing only the active filter then the required active filter length is$\begin{matrix}{l_{act}^{\prime} = \frac{c}{{nf}_{filter}}} & \text{(EQ~~3)}\end{matrix}$

The Q of this filter which is defined as

Q=ƒ _(filter)/Δƒ  (EQ 4)

and is given by $\begin{matrix}{Q = \frac{\pi}{\arccos \left( \frac{{- 1} + {2G} - {0.25G^{2}}}{G} \right)}} & \text{(EQ~~5)}\end{matrix}$

Eq (3) shows that for high f_(filter) frequencies, the required activedelay line length may become very short, and this could cause afrequency limitation. More importantly, Eq(5) shows that the only way toincrease the Q for this purely active filter is to increase the gain Gto its limiting value of 2. However, the limit to how close G can bemade to 2 is determined by practical considerations which require thatan adequate margin is maintained to prevent the onset of lasing. Thishas limited the practical Q that is realisable for the active filter toa value of around 325.

However, inspection of equation (2) also shows that the bandwidth of theresponse peaks can also be narrowed by increasing the delay time T_(act)of the active delay line. Normally this is not an option, because forthe purely active filter an increase in l_(act) also lowers thefundamental frequency of the filter below the required value off_(filter).

In the topology of a first embodiment, the delay time of the activefilter is increased by a factor N, so it operates at a fundamentalfrequency that is N times lower, but follow the active filter 5 by ap-section passive Mach-Zehnder lattice filter 6. The passive sections11,12,13 are designed so that they produce a coincident pass frequencyat Nf_(act) to select the N^(th) peak in the frequency response of theactive delay line, but have notches to eliminate all the intermediatepeaks. Hence the N^(th) peak now coincides with the specified filterfrequency f_(filter). However, now the active filter 5 is operating witha much longer delay length, which from Eq(2) means a much narrower 3 dBbandwidth will result. This results in the Q of the hybrid filter beingincreased by a least a factor of N, in comparison to the purely activeapproach, for the same amount of gain margin.

For the hybrid structure, the transfer function is given by$\begin{matrix}{{H_{c}(z)} = {K\quad \frac{Z_{act} - Z_{0}}{Z_{act} - p_{l}}{\prod\limits_{i}^{\quad}\left( {\frac{1}{2} \cdot \frac{z_{i} + 1}{z_{i}}} \right)}}} & \text{(EQ~~6)}\end{matrix}$

where z_(act) is used for the active delay line and z_(i) (i=1,2, . . .) for passive notch delay line with different delay lengths.

Now for the hybrid filter f_(1act is) chosen as

ƒ_(1act)=ƒ_(filter) /N  (EQ 7)

and thus

l _(act) =Nl′ _(act)  (EQ 8)

The 3 dB bandwidth of the response peaks of the hybrid filter is givenby $\begin{matrix}{\frac{\left( {{\cos \quad {\pi\Delta}\quad {fT}_{1}} + 1} \right)\left( {{\cos \quad \pi \quad \Delta \quad {fT}_{2}} + 1} \right)\left( {{\cos \quad \pi \quad \Delta \quad {fT}_{3}} + 1} \right)}{1 - {G\quad \cos \quad \pi \quad \Delta \quad {fT}_{act}} + {0.25G^{2}}} = \frac{4}{\left( {1 - {0.5G}} \right)^{2}}} & \text{(EQ~~9)}\end{matrix}$

where T_(i)=nl_(i)/c; l_(i); is the delay length difference of thei^(th) Mach-Zehnder passive notch filter.

The passive section delay lengths l₁, l₂, l₃ are chosen to produce acoincident pass at the N^(th) peak of the active filter whichcorresponds to f_(filter) and notches to eliminate the intermediatepeaks. Under these conditions the 3 dB bandwidth of the response peakarising from the active filter is virtually unaltered at the f_(filter)frequency and its value is very well approximated by the expression$\begin{matrix}{{\Delta \quad f} \approx {\frac{1}{N}\Delta \quad f_{act}^{\prime}}} & \text{(EQ~~10)}\end{matrix}$

The bandwidth of the fundamental peak at the filter frequency f_(filter)is now N times smaller. Hence the Q of the hybrid filter is given by$\begin{matrix}{Q = {{N\frac{f_{filter}}{\Delta \quad f_{act}^{\prime}}} = {NQ}^{\prime}}} & \text{(EQ~~11)}\end{matrix}$

Hence for the same value of gain margin, the hybrid filter gives an Ntimes increase in Q.

3. Synthesis

The design procedure for a filter which has a required fundamentalbandpass frequency of f_(filter) proceeds by setting

ƒ_(lhybrid)=ƒ_(filter)  (EQ 12)

The active filter delay length is l_(act) is next chosen to give

ƒ_(lact)=ƒ_(lhybrid)/2″=ƒ_(lhybrid) /N  (EQ 13)

where n is an integer. The choice of the value of n depends on atradeoff between the narrowness of the filter response and the number ofpassive notch filter sections required. The higher n is made, the longerthe active length that can be used, which results in a narrower responsepeak when a given gain margin is used, Eq 2. However, increasing n alsomeans that there are more intermediate peaks that must be eliminated sothat only the N^(th) peak of the response is selected, and this requiresa larger number of passive notch filters.

For a chosen value of N, there are N−1 intermediate peaks that must beeliminated. This is done with a p-section passive filter. Each sectionof the passive filter is a 2-tap FIR structure which has notchfrequencies at $\begin{matrix}{{f_{n} = {{{\left( {i + \frac{1}{2}} \right) \cdot \frac{N}{M}}f_{act}\quad i} = 0}},1,\ldots \quad,{M - 1}} & \text{(EQ~~14)}\end{matrix}$

and pass frequencies at $\begin{matrix}{{f_{p} = {{i\quad \frac{N}{M}f_{act}\quad i} = 0}},1,\ldots \quad,{M.}} & \text{(EQ~~15)}\end{matrix}$

The passive sections are chosen so that they have a coincident passfrequency at Nf_(act) to select the N^(th) peak in the frequencyresponse of the active delay line, but have notches to eliminate all theintermediate peaks from 1 to N−1. The number of passive filter sectionsp required to do this is

p=n  (EQ 16)

Finally, the passive filter Mach-Zehnder length differences required inthe p-section filter are $\begin{matrix}{{l_{passive} = {{\frac{l_{act}}{2^{n - j}}\quad {where}\quad j} = 0}},1,2,{\ldots \quad \left( {n - 1} \right)}} & \text{(EQ~~17)}\end{matrix}$

As an example, in one embodiment, N=8 was chosen, thus n=3. The requiredactive delay length is $\begin{matrix}{l_{act} = {N\quad \frac{c}{{nf}_{filter}}}} & \text{(EQ~~18)}\end{matrix}$

Hence the hybrid filter frequency corresponds to the 8^(th) peak of theactive delay line filter. A 3-section passive filter 6 is required. Thedelay length differences required in the 3-section passive filter are⅛l_(act) ¼l_(act) and ½l _(act). FIG. 2b shows the computed result forthe hybrid filter designed to have an overall bandpass response at 1.1GHz. FIG. 3 shows the computed responses for the three passive filtersections. It can be seen that the passive sections have a coincidentpass frequency 25 at the required filter frequency of 1.1 GHz butprovide notches at the lower intermediate frequencies. Because thisenables us to use an active delay line that is 8 times longer, comparedto the length required if the active filter fundamental was directly atthe specified filter frequency of 1.1 GHz, the passband peak at thefilter frequency is at least 8 times narrower, and hence the Q isincreased by at least 8 times. There is also additional rejection at outof band frequencies compared to a design using only a simple activefilter.

4. Coherence Effects

The cascading of delay lines must ensure that there are no coherentinterference effects. Hence there are requirements on the topology ofthe hybrid structure. The coherence length of laser must be less thanthe minimum delay path difference in all possible paths in the hybridstructure.

A key point about the topology shown in FIG. 1 is that it enablescascading of filters, without introducing interference problems. This isbecause the active delay line, which is an infinite impulse response(IIR) filter, is followed by finite impulse response (FIR) filters.

The multiple path lengths in the structure can be analysed by means ofthe impulse response. FIG. 4 shows the impulse response of the hybridstructure. The length of the active delay line sets the basic periodτ_(act) of pulses. The 2-tap Mach-Zehnder FIR passive sections producethe in-between pulses. The p-section filter generates 2^(p) pulses,which are equally spaced within the period τ_(act). It can be seen thatit is not possible for two pulses to arrive simultaneously, which meansthat no two paths can exist in the hybrid structure with the samelengths. The minimum pulse separation in this hybrid structure isτ_(min)=τ_(act)/N. This corresponds to the shortest delay timedifference in the structure. Hence the coherence length of the lasersource must be less than l_(act)/2^(n). This was the case in theconstructed embodiment, and no coherence interference effects werepresent.

5. Higher Order Passive Filters for Increasing the Q of the HybridFilter.

As an alternative embodiment, the Q of the hybrid filter can be furtherincreased by adding an extra passive post-filter 30 as illustrated inFIG. 5, to form the last stage. In order to sharpen the response, a lowfundamental frequency is chosen for the filter 30. Its delay lengthdifference is chosen as

l ₄ =Kl _(act)  (19)

where K is an integer. In order to avoid coherent interference effectsin this structure, a two photodetector technique is used at the output.

The 3 dB bandwidth of the peak of this combined structure is given by$\begin{matrix}{\frac{\begin{matrix}{{\left( {{\cos \quad \pi \quad \Delta \quad {fT}_{1}} + 1} \right)\quad \left( {{\cos \quad \pi \quad \Delta \quad {fT}_{2}} + 1} \right)}\quad} \\{\left( {{\cos \quad \pi \quad \Delta \quad {fT}_{3}} + 1} \right)\quad \left( {{\cos \quad \pi \quad \Delta \quad {fT}_{4}} + 1} \right)}\end{matrix}}{1 - {G\quad \cos \quad \pi \quad \Delta \quad {fT}_{act}} + {0.25G^{2}}} = \frac{8}{\left( {1 - {0.5G}} \right)^{2}}} & \text{(EQ~~20)}\end{matrix}$

Substantial narrowing of the response and hence increase in Q. can beobtained with the inclusion of the post-filter 30 with a large delaydifference.

6. Implementation and Results

The hybrid filter structure 1 shown in FIG. 1, was set up to operate ata fundamental frequency of 1.1 GHz. The active delay line filter 5comprised a 50% reflectivity grating 9 and a 100% reflectivity grating 8at the signal wavelength of 1558 nm, and each had a spectral width of0.5 nm. The parameter N (=2″) of the hybrid filter was chosen as 8.Hence the fundamental frequency of the active filter was 0.14 GHz, andthis corresponds to a single pass optical delay of 73 cm for the activefilter. This structure has practical dimensions, and was implementedwith erbium doped active fibre pumped by a 980 nm laser 7.

The number of passive sections 11,12,13 required p=n=3, and this wasimplemented with unbalanced Mach-Zehnder sections, with lengthdifferences for each section as given by Eq (17). The delay line lengthdifferences need to be implemented accurately so that the notchfrequencies match the peaks to be eliminated, however this is notdifficult to implement because the tolerances are within the RFwavelength. The coherence length of the laser source was less than theshortest delay difference in the hybrid filter and the signal wavelengthwas 1558 nm.

FIG. 6 shows, as a reference, the measured frequency response of theactive filter embedded in the hybrid structure. This has fundamentalfrequency of 141 MHz, as expected. The measured 3 dB bandwidth of thepeak is 1.475 MHz. Using Eq 2, this corresponds to a double pass opticalgain of G=1.935, which provides an ample gain margin from lasing andgives very stable operation.

The measured frequency response of the hybrid filter, comprising theactive delay line and 3 passive filter sections, is shown in FIG. 7. Thefundamental frequency of the response peak 40 is 1.13 GHz, and its 3 dBbandwidth is 1.41 MHz. The resulting Q value is 801.4. In a comparisonbetween the measured and predicted (using Eq. 9) values of bandwidth andQ, excellent agreement was found.

FIG. 8 shows the measured frequency response of the hybrid filterincluding a post-filter 30, as displayed in FIG. 5. The path lengthdifference in the post-filter is l_(Δ)=36 l_(act). The measured 3 dBbandwidth of the peak is reduced to 1.15 MHz, and the Q is increased to982.6, however the skirt selectivity is not as high because of thelimited selectivity of the post-filter. This shows that the post-filtercan effectively sharpen the response of the hybrid processor even more.The following table shows a comparison between measured and predicted(using Eq. 20) values of bandwidth and Q and this displays excellentagreement:

f_(1st)(MHz) Δf_(3dB)(MHz) Q Hybrid with L_(Δ) (Measured) 1130.0 1.150982.6 Hybrid with L_(Δ) (Measured) 1128 1.145 986.6

It can therefore be seen that the preferred embodiments provide for anew hybrid active-passive photonic signal processor, which achieveshigh-Q microwave bandpass filtering. This results in both a largeincrease in Q and a high frequency of operation. The structure is basedon a hybrid approach comprising both active and passive sections. Theactive section, is operated at a sub-multiple of the desired filterfrequency, and thus achieves a much narrower 3 dB bandwidth response,for a given gain margin. The passive sections eliminate the intermediatepeaks and select the multiple corresponding to the desired filterfrequency. This concept has the advantage of keeping the narrowerbandwidth that can be produced with the longer active delay length,while still operating at a much their frequency. It thus significantlyreduces the limit of lasing threshold of the active delay line, andenables the processor to function with a large gain margin, yet stillproduces a high Q. This results in very robust operation, together withhigh resolution filtering.

The general synthesis procedure for the hybrid filter has been describedand an embodiment experimentally verified by demonstrating an activefilter operating at the 8^(th) sub-multiple of the frequency, and a3-section passive filter. This novel filter, operating at a fundamentalfrequency of 1.1 GHz, exhibited a Q of 801. Moreover, using an extensionto this principle to include an additional passive optical stage,results demonstrated a narrowband filter response with a Q of 983. Thishybrid structure is simple, and the passive sections can be implementedwith simple fibre delay lines. The hybrid filter topology offershigh-resolution microwave optical signal processing with hightime-bandwidth operation.

Turning now to FIG. 9, in an alternative embodiment, the filter 80comprises optical planar integrated circuits 82, 84 for the active andpassive filter component respectively.

The RF modulated light signal 86 is coupled into a planar waveguide 88of the active filter circuit 82. The planar waveguide 88 comprises twowaveguide gratings 90, 92 between which an erbium doped portion of theplanar waveguide 88 is provided as the active delay line path betweenthe gratings 90, 92. The first grating 90 has a reflectivity of 50%,whereas the second grating 92 has a reflectivity of 100%.

A pump laser signal 96 from a pump laser 98 is coupled into a planarwaveguide 100 of the active filter circuit 82 and is coupled to thewaveguide 88 by means of a WDM coupler 102.

A 3 dB coupler 104 is used to forward the output from the active filtercircuit 82 to the passive filter circuit 84.

The passive filter circuit 84 consists of a cascade of filters 106, 108,110, which each comprise optical waveguide delay lines between 3 dBcouplers 112, 114, 116 and 118 of the passive filter circuit 84, withthe processed light signal 120 being coupled out of the planar passivefilter circuit 84.

The active and passive filter circuits are formed on separatesubstrates, which could for example be silica glass. However, it will beappreciated by a person skilled in the art that other suitablesubstrates may be used and/or that the active and passive integratedcircuits can be provided on a single substrate.

It would be appreciated by a person skilled in the art that numerousvariations and/or modifications may be made to the present invention asshown in the specific embodiments without departing from the spirit orscope of the invention as broadly described. The present embodimentsare, therefore, to be considered in all respects to be illustrative andnot restrictive.

We claim:
 1. A bandpass signal filter for filtering modulationfrequencies of a modulated optical input signal, comprising: a photonicbandpass active filter arranged in use to operate at a fundamentalfrequency which is a sub-multiple of a desired filter frequency of thebandpass filter; and a photonic passive filter arranged in use toeliminate all intermediate pass bands in the frequency response of theactive filter except the pass band at the desired filter frequency forproviding the pass band signal of the bandpass filter.
 2. A bandpassfilter as claimed in claim 1 wherein said bandpass filter operates atmicrowave frequencies.
 3. A bandpass filter as claimed in claim 2wherein the input signal is modulated by a microwave frequency opticaloscillator.
 4. A bandpass filter as claimed in claim 1, wherein saidpassive filter comprises a number of passive filter elements eachcomprising a notch filter which in combination, have high attenuationcharacteristics for frequencies outside said desired filter frequencyand low attenuation of said desired filter frequency.
 5. A bandpassfilter as claimed in claim 4 wherein the number of passive filterelements is
 3. 6. A bandpass filter as claimed in claim 1, furthercomprising a post filter interconnected to said passive filter, saidpost filter element providing for further rejection of non desiredfilter frequencies.
 7. A bandpass filter as claimed in claim 1, whereinsaid active filter comprises an infinite impulse response filter andsaid passive filter comprises a finite impulse response filter.
 8. Abandpass filter as claimed in claim 1, formed from optical fibrecomponents.
 9. A bandpass filter as claimed in claim 1, formed fromoptical planar integrated circuits.
 10. A photonic signal processorhaving a bandpass signal filter as claimed in claim 1, wherein saidphotonic signal processor has a quality factor in excess of about 500.